Martinez suffered the injury during Chelsea's 2-0 win over Everton on Saturday and was taken to hospital following a collision with defender Jarrad Branthwaite.
"He's been better; he had the surgery. We still need to wait. (He will be out for) a few weeks. Hopefully less than more," Alonso told a press conference on Friday.
Mike Penders is expected to start against Spurs. "He is ready," Alonso said. "He has been training well and played a couple of cup games where he showed he has a good level ... when he came on against Everton, he showed in a few minutes his personality and qualities."
The Chelsea boss also provided an update on Malo Gusto and Pep Chavarria, who missed last weekend's victory due to illness and injury, respectively.
"Malo (Gusto) is fine. Pep (Chavarria) is training a little bit more but he is not going to make it," the Spaniard said.